By partial drop, if you mean taking admission somewhere & preparing for JEE, probably you’ve submitted your school TC-( transfer certificate) in this particular college. When you will visit your college (NIT) for document verification, your TC is required. Since it’s already submitted somewhere else you have one option. You need to visit this college and get your TC from this college ( will be a different document mentioning that you were a student there for that particular no. or months). You can submit that in your NIT for verification. Nothing to worry it’s just to make sure that you’re not a student anywhere else. Usually, when you take admission in home state colleges they don’t take your migration, that’s an advantage as you will be having it with you (given from school). That would be needed to be submitted in NIT.
I wasn’t asked for a “Gap certificate” or whatsoever it’s named as when I took admission. This TC from ex-college is sufficient, nothing to worry about.